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Mul)ferroics  

Dr.  Tanmoy  Mai)  MSE  689  

Acknowledgement  

             Some  lecture  slides  are  borrowed  from    

               Dr.  Daniel  Khomskii  :  APS  fellow,    A  famous  Russian  physicist                  -­‐-­‐    currently    in  Cologne  University,  Germany  

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Ferroics  

Ferroelectric materials possess a spontaneous polarization that is stable and can be switched hysteretically by an applied electric field; antiferroelectric materials possess ordered dipole moments that cancel each other completely within each crystallographic unit cell.  

Ferromagnetic materials possess a spontaneous magnetization that is stable and can be switched hysteretically by an applied magnetic field; antiferromagnetic materials possess ordered magnetic moments that cancel each other completely within each magnetic unit cell.  

There are three types of primary ferroics:!

Ferroelastic materials display a spontaneous deformation that is stable and can be switched hysteretically by an applied stress.  

Dr.  Tanmoy  Mai)  

• Multifunctional Material possess multiple order parameters!• Multiferroic Materials possess two or more of the following!

• (Anti-)Ferromagnetism, (Anti-)Ferroelectricity, !! (Anti-)Ferroelasticity!

Introduction to Multiferroics !

Before  applied  field  

During  and  aHer  applied  

field  

field  

• Coupling between order parameters!

Hσ

M

P

ε

Magnetoelasticity!

χE

χM S

dE

α

E

dM

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The   combina,on  of  magne,c  proper,es  with  dielectric,   semiconduc,ng,  or  ferroelectric   materials   allows   for   the   design   of   materials   with   novel  func,onali,es  and  provides  the  basis  for  various  device  applica,ons.     In   the   same   material   (e.g.   magne,c   semiconductors   (MS)   or   intrinsic  mul,ferroics)     In   ar,ficial   heterostructures   (e.g.   ferromagne,c/dielectr ic  heterostructures  for  magne,c  tunnel  junc,ons  (MTJs)  or  ar,ficial  mul,ferroic  heterostructures)  

An obvious approach for the realization of oxide materials with improved functionality is the integration of two properties in one and the same material.!

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Dr.  Tanmoy  Mai)  

but  the  real  beginning  of  this  field  started  in  1959  with  a  short    

remark   by   Landau   and   Lifshitz   in   a   volume   of   their   Course   of  Theore)cal  Physics:  

“Let   us   point   out   two   more   phenomena,   which,   in  principle,   could   exist.   One   is   piezomagne)sm,   which  consists  of  linear  coupling  between  a  magne)c  field  in  a   so l id   and   a   deforma)on   (ana logous   to  piezoelectricity).   The   other   is   a   linear   coupling  between  magne)c  and  electric  fields  in  a  media,  which  would   cause,   for   example,   a   magne)za)on  propor)onal   to   an   electric   field.   Both   these  phenomena   could   exist   for   certain   classes   of  magnetocrystalline  symmetry.”  

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Hysterisis Loop!

Ferromagnetism.!  Display spontaneous

magnetization."  Produce Hysterisis Loop."  Can be found mainly in metals."

Ferroelectricity.!  Display spontaneous

polarization."  Produce Hysterisis Loop."  Ferroelectrics are insulators"

H, E

Dr.  Tanmoy  Mai)  

Ferro-­‐electric/magne)c    

Multiferroics  Electric and magnetic ordering in solids are usually

considered separately: effects such as ferroelectricity are caused by charges while magnetism is caused by Spins.

 However, in a few cases these two orders are strongly coupled. If this is the case, then it may occur that using an electric field E, we can induce a finite magnetization M. Or using a magnetic field H, we can generate a finite electric polarization P.

 If a material has both orders, namely nonzero P and M, using H we could control P or using E we can control M.

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Dr.  Tanmoy  Mai)  

Reviews  

•  Sang  Cheong  and  Maxim  Mostovoy,  MulFferroics:  a  magneFc  twist  for  ferroelectricity,  Nature  Materials  6,  13  (2007).  

•  R.  Ramesh  and  Nicola  Spaldin,  MulFferroics:  progress  and  prospects  in  thin  films,  Nature  Materials  6,  21  (2007).  

•  D.  Khomskii,  Physics  2,  20  (2009).  

•  Special  issue  of  Journal  of  Physics:  Condensed  Ma`er,  vol  20,  number  43,  29  Oct  2008.  

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Induction of magnetization by an electric field; induction of polarization by a magnetic field.

- first presumed to exist by Pierre Curie in 1894 on the basis of symmetry considerations

However, the effects are typically too small to be useful in applications!

Magnetoelectric effect

Materials exhibiting ME effect: Cr2O3 BiMnO3 BiFeO3 …..

M. Fiebig, J. Phys. D: Appl. Phys 38, R123 (2005)

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Magnetoelectric Multiferroics Materials!Cr2O3 !

• Prototypical ME, first discovered!

• P and M are field induced!

• αZZ = 4.13 ps m-1 @ E = 106 V!

• Corresponds to the magnetization observed after reversal of only 5 of every 106 spins in the AFM lattice!!!

Other ME Materials!

• Ti2O3!

• GaFeO3!

• Boracites and Phosphates!

• PbFe0.5Nb0.5O3!

• Garnet films!

• ~80 total materials have ME effects!

Top Performers !

• LiCoPO4 (αYX = 30.6 ps m-1)!

• Y3Fe5O12 films (α ~ 30 ps m-1)!

• TbPO4 (αAA = 36.7 ps m-1)!

! Principal weakness of ME Effect Perturbative nature of the microscopic

mechanisms driving ME behavior!

and ME response is limited by!

αij2 < χii

e χjjm!

Where χiie and χjj

m are the electrical and magnetic susceptibilities!

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(Ferro)magnetism vs. (Ferro)electricity Perovskite structure

(La,Sr)MnO3: spins from : 3d3 or 3d4

BaTiO3: polarization from cation/anion paired diploes

O-2

Ti+4

Magnetic moment:

- Ba+2

0.10 Å

0.05 Å 0.04 Å

+

+ Ti 3d0 O 2p2

unfilled d bands impurities

inversion symmetry broken Dr.  Tanmoy  Mai)  

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•  BiMnO3, BiFeO3, Pb(Fe2/3W1/3)O3:

6s2 lone pairs off-center distortion polar behavior

Mechanism of ferroelectricity

• PbTiO3: Pb-O covalent bond

cubic 800 K

tetragonal 300 K

Pb-O plane Ti-O plane

Pb

O

Kuroiwa et al, PRL87 217601 (2001)

Dr.  Tanmoy  Mai)  

Materials  compa)bility  

FE:        d0  

Pb(Ti,  Zr)O3  (PZT)  Covalent  bonding  between  d0  and  O.    This  mechanism  is  not  compa)ble  with  magne)sm  

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1.  

2.  

3.  

4.  

5.  

How  to  combine  magne,sm  and  ferroelectricity:        Different  types  of  mul,ferroics

In  charge  ordered  systems,  the  coexistence  of  inequivalent  sites  with  different  charges,  and  inequivalent  (long  and  short)  bonds,  leads  to  ferroelectricity.  

e.g.  Ni-­‐I  boracite  (Ni3B7O13I)  

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6.  

7.  

How  to  combine  magne,sm  and  ferroelectricity:                  Different  types  of  mul,ferroics

There are two types of multiferroics:

(1)  Proper (or type I) multiferroics. In these cases the two phenomena of P and M occur for different reasons, but there is still a (weak) coupling between them. A famous example is BiFeO3, with TFE=1100K and TAF=643K.

(2) Improper (or type II) multiferroics. New developments. Here both orders are deeply coupled to one another. But unfortunately critical temperatures are small. In spite of this problem for applications, they are the most interesting intellectually.

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“Type  I”  vs.  “Type  II”  MF  BiFeO3  

TbMn2O5  

The  magne,c  and  the  “polar”  site  are  dis,nct  –  2  different  mechanisms  for  FE&FM.    TFE>>TC/TN>RT,  but  the  coupling  is  very  weak,  usually  through  magneto-­‐stric)on.  

The  polarisa)on  is  generated  by  the  magne,c  ordering.  dis)nct.  Weak  FE  and  RT  >TFE=TN,  but  the  coupling  is  very  large  (“Colossal”  effects).  

Phys.  Rev.  Le`.  94,  117203  (2005)    

Magneto-­‐Electric  coupling  

Linear  Magnetoelectrics    (Cr2O3)  

P  

H  

P  M/Ms  

TE  TC/TN  

“Type  I”  mul,ferroics    (YMnO3)  

P          Ms  

TN=TE  

“Type  II”  mul,ferroics    (TbMnO3)  

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“Type  II”  Mul)ferroics  

P          Ms  

TN=TE  

1,  2,  m,  mm2,  4,  4mm,  3,  3m,  6,  6mm  

Common  Ingredient:  PG  symmetry  must  be  lowered  to  one  of  the  10  pyroelectric  groups.  

Mul)ferroic  Materials    

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“Type  I”  Mul)ferroics  

P  M/Ms  

TE  TC/TN  

Fe

Bi

(001)  

AFM Ordering

FE Ordering

Polariza,on  points  in  one  of  8  possible  <111>  direc,ons.  

Magne,c  plane  is  perpendicular  to  the  polariza,on  direc,on.  

P

Bi  

Fe  

O  

M

M

BiFeO3 : only room temp multiferroic!

TC  ~  1103K  TN  ~  643K  

Bulk

Ederer and Spaldin, PRB 71(2005)

G-­‐type  an)ferromagnet  

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A-­‐type:  The  intra-­‐plane  coupling  is  ferromagne?c  while  inter-­‐plane  coupling  is  an?ferromagne?c.  

C-­‐type:  The  intra-­‐plane  coupling  is  an?ferromagne?c  while  inter-­‐plane  coupling  is  ferromagne?c.  

G-­‐type:  Both  intra-­‐plane  and  inter-­‐plane  coupling  are  an?ferromagne?c.    

Expected magnetic behavior!

P <111>  

-­‐110  

-­‐211  

-­‐101  

-­‐12-­‐1  

01-­‐1  11-­‐2  

x  y  

z  

P  

P   P  

Ferroelectric  domain  

Easy  Magne,c  Axis  

AFM  domain  

Might  there  be  a  preferred  axis?  

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Electrical Control!P1

+ Bi  

Fe  

O  

*  F.  Kubel,  H.  Schmid,  Acta  Cryst.  B46,  698  (1990)    

E

P1-

P4-

109°   P3-

8 possible polarization variants

3 types (180°, 71° and 109°)  of ferroelectric polarization

switching

T.  Zhao,  M.  Barry  et  al.,  Nat  Mat  5,  823  (2006)  

BiFeO3  SrRuO3  SrTiO3  

C.  Ederer  and  N.  A.  Spaldin,  PRB  71,  060401(2005)  

BiFeO3  

TC  =    1,100  K  TN=      640  K.  

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Geometric ferroelectrics: hexagonal RMnO3

BaNi(Mn,Co,Fe)F4 For example: YMnO3: A-type AF, lacking lone pairs, no chemically active bonding to produce ferroelectricity  Buckling of MnO5 pyramids  Symmetry allows Y-O distance change, hence displacement of Y : net polarization

Origin of ferroelectricity

van Aken et al., Nature Materials 3, 164, (2004)

Y

MnO5

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Site-centered charge order

•  Electronic ferroelectrics: Combination of bond-centered and site-centered charge order

Efremov et al., Nature Materials 3, 853, (2004)

Bond-centered charge order Ferroelectric

intermediate state

O  

TM  

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Recent Discoveries  

•  Frustrated magnetic systems. •  The magnetic phases are complicated; incommensurate AF orders seem to be common. •  Strong coupling between ferroelectricty and magnetism.

TbMnO3, Nature 426, 55, (2003); PRL 95, 087206 (2005).

RMn2O5,  Nature 429, 392 (2004) (Tb);

PRL 96, 067601 (2006)   (Y).  

TbMnO3  

Kimura  T,  et.al,    Nature  426,  55  (2003).   PRB  68,  060403(R)  (2003).    

J1  

J2  

J3  

 Orthorhombically  distorted  perovskite  structure  (space  group  Pbnm)   the  perovskite  TbMnO3  does  not  contain  6s  lone  pairs,  which  produce  a  polar  structure  in  magne)c  ferroelectric  perovskites  BiMnO3  and  BiFeO3   Mn3+  ions  with  occupied  d  orbitals  

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T=35 K

T=15 K

TN=42 K

TC=27 K

TbMnO3

Kenzelmann et al., PRL 95, 087206 (2005)

IC sinusoidally modulated collinear magnetic order, inversion symmetric

IC non-collinear magnetic order, inversion symmetry broken

Long  wavelength  incommensurate  AF  spin  ordering␣                      coupled  to  lalce  to  produce  inversion  symmetry  breaking  

The  effect  of  spin  frustra,on  causes  sinusoidal  an,ferromagne,c  ordering.  The  modulated  magne,c  structure  is  accompanied  by  a  magnetoelas,cally  induced  lalce  modula,on,  and  with  the  emergence  of  a  spontaneous  polariza,on.  

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Conclusions  •  Magne)c  mul)ferroics  are  a  lot  more  common  than  previously  

thought!    In  fact,  the  development  of  a  small  polariza)on  may  be  ubiquitous  given  an  appropriate  magne)c  symmetry.  

•  Mul)ferroics  are  fascina)ng  materials  and  they  may  even  be  useful…    They  definitely  made  (re)learn  some  very  clever  physics.    

•  More  generally,  mul)ferroics  remind  us  that  most  interes)ng  physical  proper)es  emerge  from  (point)  group  symmetry  breaking  (“Neumann”  tensors).    

The  theory  (and  prac,ce)  of  symmetry    is  key  to  all  new  materials  proper,es.  

Exotic results already found

•  The interface between two insulators can be a metal

•  The interface between two insulator can be a superconductor

•  In general, the properties of the ensemble can be drastically different from the properties of the individual building blocks

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nature  materials  VOL  7,  Page  478  JUNE  2008  

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Sketch of a possible MERAM element. The binary information is stored by the magnetization direction of the bottom FM layer (blue), read by the resistance of the magnetic trilayer (Rp when the magnetizations of the two FM layers are parallel), and written by applying a voltage across the multiferroic FE –AFM (green) layer . If the magnetization of the bottom FM layer is coupled to the spins in the multiferroic (small white arrows) and if the magnetoelectric coupling is strong enough, reversing the FE polarization P in the multiferroic changes the magnetic configuration in the trilayer from parallel to antiparallel, and the resistance from Rp to antiparallel (Rap).

nature  materials  |  VOL  7  |  Page  425,  JUNE  2008